Given that z[itex]_{1}[/itex]z[itex]_{2}[/itex] ≠ 0, use the polar form to prove that
Re(z[itex]_{1}[/itex][itex]\bar{z}[/itex][itex]_{2}[/itex]) = norm (z[itex]_{1}[/itex]) * norm (z[itex]_{2}[/itex]) [itex]\Leftrightarrow[/itex] θ[itex]_{1}[/itex] - θ[itex]_{2}[/itex] = 2n∏, where n is an integer, θ[itex]_{1}[/itex] = arg(z[itex]_{1}[/itex]), and θ[itex]_{2}[/itex] = arg(z[itex]_{2}[/itex]). Also, [itex]\bar{z}[/itex][itex]_{2}[/itex] is the conjugate of z[itex]_{2}[/itex].

2. Relevant equations

norm (z) = [itex]\sqrt{a^{2} + b^{2}}[/itex], where z = a +i*b.

norm (z) = r, where r is the radius.

z = r[cos θ + i*sin θ]

3. The attempt at a solution

Trying to prove the forward direction, I know the above formulas, and that arg(z[itex]_{1}[/itex]z[itex]_{2}[/itex]) = θ[itex]_{1}[/itex] + θ[itex]_{2}[/itex] +2n∏.
I'm having trouble getting the first step. I know that norm (z[itex]_{1}[/itex]) * norm (z[itex]_{2}[/itex]) = r[itex]_{1}[/itex]r[itex]_{2}[/itex], but I don't know if this is how you begin.

Given that z[itex]_{1}[/itex]z[itex]_{2}[/itex] ≠ 0, use the polar form to prove that
Re(z[itex]_{1}[/itex][itex]\bar{z}[/itex][itex]_{2}[/itex]) = norm (z[itex]_{1}[/itex]) * norm (z[itex]_{2}[/itex]) [itex]\Leftrightarrow[/itex] θ[itex]_{1}[/itex] - θ[itex]_{2}[/itex] = 2n∏, where n is an integer, θ[itex]_{1}[/itex] = arg(z[itex]_{1}[/itex]), and θ[itex]_{2}[/itex] = arg(z[itex]_{2}[/itex]). Also, [itex]\bar{z}[/itex][itex]_{2}[/itex] is the conjugate of z[itex]_{2}[/itex].

2. Relevant equations

norm (z) = [itex]\sqrt{a^{2} + b^{2}}[/itex], where z = a +i*b.

norm (z) = r, where r is the radius.

z = r[cos θ + i*sin θ]

3. The attempt at a solution

Trying to prove the forward direction, I know the above formulas, and that arg(z[itex]_{1}[/itex]z[itex]_{2}[/itex]) = θ[itex]_{1}[/itex] + θ[itex]_{2}[/itex] +2n∏.
I'm having trouble getting the first step. I know that norm (z[itex]_{1}[/itex]) * norm (z[itex]_{2}[/itex]) = r[itex]_{1}[/itex]r[itex]_{2}[/itex], but I don't know if this is how you begin.